1. Field of the Invention
The present invention relates to determining a property of an earth formation, and in particular to measuring acoustic waves to determine the property.
2. Description of the Related Art
Obtaining accurate formation compressional and shear velocity from acoustic logging measurements is important for various geophysical and petroleum engineering applications. A challenge for processing acoustic data, whether the data is from wireline or LWD (logging while drilling) measurements, is how to correctly handle the dispersion effect of the waveform data, because the dispersion effect is the fundamental nature of elastic wave propagation in a waveguide such as a borehole penetrating an earth formation. In general, the wave dispersion characteristics are governed by the dispersion equation (Tang, X., Wang, T. and Patterson, D., 2002, Multipole acoustic logging-while-drilling, 72nd Ann Internat. Mtg: Soc. of Expl. Geophys., 364-367):D(k, ω, Model)=0  (1)where k is wavenumber and w is angular frequency, and “Model” refers to the borehole waveguide structure model consisting of borehole fluid, formation, and a logging tool. For example, in the case of LWD, the structure model includes an LWD acoustic tool that occupies a large part of the borehole. The presence of the LWD tool significantly changes the dispersion characteristics, as compared to the wireline case where the tool effect is less significant. Solving the dispersion equation for each frequency, we find the wavenumber k for a guided wave mode, from which the wave phase velocity or slowness (inverse of velocity) is obtained asV(ω)=ω/k, or S(ω)=1/V(ω)=k/ω  (2)
Using the above approach we can calculate the theoretical dispersion curve for the wireline dipole-flexural waves (Schmitt, D. P., 1988, Shear-wave logging in elastic formations: J. Acoust. Soc. Am., 84, 2215-2229) and LWD quadrupole waves (Tang et al., 2002), etc. The above dispersion equation can also be used to calculate the dispersion curve for leaky-P waves, whose dispersion effect becomes quite significant for acoustic logging in a low-velocity formation (for wireline case, see Hornby, B. E., and Pasternark, E. S., 2000, Analysis of full-waveform sonic data acquired in unconsolidated gas sands: Petrophysics, 41, 363-374; for LWD case, see Tang, X. M., Zheng, Y., and Dubinsky, V., 2005, Logging while drilling acoustic measurement in unconsolidated slow formations, paper R, in 46th Annual Logging Symposium Transactions, Society of Professional Well Log Analysts).
The theoretical dispersion equation shows that the dispersion curve of a guided wave involves numerous model parameters. Even in the simplest case of a fluid-filled borehole without tool, six parameters are needed to calculate the dispersion curve (i.e., borehole size, formation P- and S-velocities and density, and fluid velocity and density). In an actual logging environment, other unknown or uncontrollable influences (or parameters), such as changing fluid property, tool off-centering, borehole rugosity, formation alteration, etc., can also alter the dispersion characteristics. Because of these complexities, modeled-based dispersion estimation (e.g., Kimball, C. V., 1998, Shear slowness measurement by dispersive processing of borehole flexural mode: Geophysics, 63, 337-344; Geerits, T. W. and Tang, X., 2003, Centroid phase slowness as a tool for dispersion correction of dipole acoustic logging data: Geophysics, Soc. of Expl. Geophys., 68, 101-107) may suffer significant errors if the borehole condition is far from the assumed ideal theoretical condition.
To address the drawbacks of the model-based dispersion estimation methods, a data-driven method was recently developed (Huang, X., and Yin, H., 2005, A data-driven approach to extract shear and compressional slowness from dispersive waveform data: 75th Annual International Meeting, SEG, Expanded Abstracts, 384-387) and subsequently improved in the data processing practice (Zheng, Y., Huang, X., Tang, X., Patterson, D., and Yin, H., 2006, Application of a new data-driven dispersive processing method to LWD compressional and shear waveform data, Paper 103328, SPE Annual Technical Conference and Exhibition). The data driven method does not use the full theoretical modeling. Instead, it uses a common characteristic of guided waves. That is, at low frequencies, the dispersion curve of a guided wave becomes flat and reaches the formation (P or S) velocity. The flat portion of the curve, when discretized and counted over small frequency intervals, tends to have higher probability of event occurrence over the steep portion of the curve. Thus, by projecting the counted events onto the slowness axis to form a population distribution, or histogram, and detecting edge of the peak distribution, the true formation slowness that is free of dispersion effect can be estimated. A drawback of the histogram approach is that data noise and/or mode interference tend to create spurious histogram peaks and mislead the edge detection process.
Therefore, what are needed are techniques to determine accurate compressional and shear velocity of an earth formation. Preferably, the techniques use an accurate dispersion estimation method.